Given the current low volatility environment, I’ve been doing some research and application on the material in Jeff Augen’s Volatility Edge. What I’m hoping to accomplish is a more informed action plan for short-term trading using primarily options on SPX, VIX, and JNUG. In an earlier chapter in Augen’s book, he mentions that it is worthwhile to construct a distribution for price deviations (calculated using short-term return volatility) to determine whether it would be more acceptable to long the puts or calls for an underlying security. These price deviations are calculated by taking the daily dollar change of the security and dividing it by the estimated rolling standard deviation of dollar price change (calculated first by taking the standard deviation of the log returns of the stock) to see whether there are any discrepancies in its return distribution.

I decided to conduct this exercise on the above mentioned indices as well as JNUG since this highly volatile instrument makes for good short term trading. I’ve constructed the following visualisations as a reference to see whether a security is tending towards a bullish or bearish trend. Each image is a collection of four charts with the top left showing the daily price deviations, the top right showing a histogram of price deviations given the time frame, and the bottom two charts as just a magnification of the histogram either on the negative or positive deviations. I decided to use a 20 day rolling window for standard deviations since I’m intending on using this information for short-term trading; the entire time frame is 756 days. As well, the Daily Price Deviations chart only shows the most recent 60 days of movements to give a better current idea.

**SPX Price Deviations**

- Date of largest negative spike: 09/09/2016 (-8.29 std)
- Date of largest positive spike: 11/07/2016 (5.31 std)

**VIX Price Deviations**

- Date of largest negative spike: 11/09/2016 (-3.27 std)
- Date of largest positive spike: 09/09/2016 (8.55 std)

**JNUG Price Deviations**

- Date of largest negative spike: 07/20/2015 (-5.47 std)
- Date of largest positive spike: 12/29/2016 (3.15 std)

To get a numerical understanding of the distributions, I’ve also created the following two tables showing the exact occuring frequency and percentage frequency of price deviations for the above securities.

Price Deviation Bins | SPX Frequency | VIX Frequency | JNUG Frequency |
---|---|---|---|

-9 | 1 | 0 | 0 |

-8 | 0 | 0 | 0 |

-7 | 1 | 0 | 0 |

-6 | 0 | 0 | 1 |

-5 | 2 | 0 | 0 |

-4 | 7 | 2 | 4 |

-3 | 18 | 15 | 21 |

-2 | 76 | 81 | 88 |

-1 | 255 | 301 | 263 |

0 | 267 | 237 | 248 |

1 | 112 | 81 | 111 |

2 | 13 | 24 | 18 |

3 | 3 | 7 | 2 |

4 | 0 | 2 | 0 |

5 | 1 | 4 | 0 |

6 | 0 | 1 | 0 |

7 | 0 | 0 | 0 |

8 | 0 | 1 | 0 |

Price Deviation Bins | SPX Frequency | VIX Frequency | JNUG Frequency |
---|---|---|---|

-9 | 0.1% | 0.0% | 0.0% |

-8 | 0.0% | 0.0% | 0.0% |

-7 | 0.1% | 0.0% | 0.0% |

-6 | 0.0% | 0.0% | 0.1% |

-5 | 0.3% | 0.0% | 0.0% |

-4 | 0.9% | 0.3% | 0.5% |

-3 | 2.4% | 2.0% | 2.8% |

-2 | 10.1% | 10.7% | 11.6% |

-1 | 33.7% | 39.8% | 34.8% |

0 | 35.3% | 31.3% | 32.8% |

1 | 14.8% | 10.7% | 14.7% |

2 | 1.7% | 3.2% | 2.4% |

3 | 0.4% | 0.9% | 0.3% |

4 | 0.0% | 0.3% | 0.0% |

5 | 0.1% | 0.5% | 0.0% |

6 | 0.0% | 0.1% | 0.0% |

7 | 0.0% | 0.0% | 0.0% |

8 | 0.0% | 0.1% | 0.0% |

What I think can be inferred from the above is that:

- For SPX, we see that price deviations are centred around 0 to -1 standard deviations. With positive returns being relatively larger than negative returns on average, but in terms of large spikes, the negative spikes are larger in magnitude than the positive spikes.
- For VIX, we see that index is clearly indicating more negative short-term price movements.
- For JNUG, it appears that positive return spikes are more frequent than negative return spikes. However, negative return spikes are larger in magnitude compared to the positive side.